Often a polygonal term is placed in front of the polyhedron name to indicate face shape. For example, a pentagonal tetracontahedron is a polyhedron of 40 faces, each with 5 sides. Beyond indicating the number of sides on each face, these face descriptors may refer to the shape of each face. Rhombic polyhedron and trapezoidal polyhedron for instance.

You might also see the term -kis at the end of a (numerical) face descriptor. This indicates that the polyhedron in question has been formed by taking a simpler polyhedron and dividing each face into several isosceles triangles.
For example. an icositetrahedon (24 sides) could be formed by taking a cube and dividing each face into 4 triangles, resulting in a tetrakis cube. In this case, the tetra- is redundant so this shape could just be called a kis cube.